How to prove that time slow down on all type of clocks?

Question

I read about time dilation and how to prove time dilation existence with light clock.

But how to prove that time slow down on all other type of clocks (biological, mechanical, digital, electric, atomic, etc.)? Is it possible to test it on real experiments?

Thanks.

You have to think about what it means to prove. The experimental verification of relativity never uses light clocks, and yet obtains agreement. Is that enough? It is usually taught from Einstein's light clock ideas, but things are usually clearer from Minkowski's spacetime diagrams, that the conclusions are much more general, than specifically about light. — naturallyInconsistent, Jun 22 '23 at 12:43
Related: https://physics.stackexchange.com/q/570966/123208 & https://physics.stackexchange.com/q/699949/123208 — PM 2Ring, Jun 22 '23 at 12:49
In the end, for physics, the experimental tests are the proof. — John Doty, Jun 22 '23 at 13:08
Does this answer your question? Why is the photon clock equivalent to all clocks? — WillO, Jun 22 '23 at 14:19
Nobody can "prove it" - it is up to you or someone else to prove it wrong! You will need to convince people that know from real life experience that the theory works, so don't expect it to be easy. — m4r35n357, Jun 22 '23 at 16:14

Dale · Answer 1 · 2023-06-22T16:20:54.900

But how to prove that time slow down on all other type of clocks (biological, mechanical, digital, electric, atomic, etc.)?

This is a simple and direct application of the principle of relativity.

Suppose first that we have a light clock and some other clock that are both located at the same place and are moving inertially together. Suppose further that they tick at the same rate in their rest frame.

Now, we construct a second pair of clocks identically to the first pair, and this other pair is moving inertially relative to the first pair.

If the second pair did not tick at the same rate in their rest frame, then we could experimentally distinguish the first reference frame from the second reference frame, in violation of the first postulate. Therefore the second pair must also tick at the same rate in the second frame.

Now, we know that the light clock undergoes time dilation, and we know that the other clocks tick at the same rate as the light clock. Therefore the other clock must undergo time dilation also.

Is it possible to test it on real experiments?

Yes, this has been tested using many different kinds of clocks. We have used atomic clocks, decaying muons, astronomical clocks, other decaying particles, nuclear transitions, etc. All demonstrate time dilation.

score 3 · Accepted Answer · answered Jun 22 '23 at 14:40

You misunderstand time dilation. It is not an effect that 'slows down clocks'. Time dilation refers to the fact that the interval between two events that occur in the same place in one frame is less than the interval between the two events in a frame in which they occur in two different places. For example, if you sing a song that lasts two minutes in your car while you are driving, then in the frame of a passing pedestrian your song will last slightly more than two minutes. The start and end of the song happen in the same place in the frame of your car, but they happen in two different places in the frame of the pedestrian.

Note that it is the interval itself that changes- it has nothing to do with clocks. If you sing a song that lasts 100 seconds in your car, then in the frame of a passing spaceship it might last 200 seconds. An accurate clock in your car will tick off the 100 seconds and accurate clocks in the frame of the spaceship will say the song lasted 200 seconds because it did, not because the clocks are running fast.

The difference in the intervals is a property of the geometry of spacetime.

I read on Wiki https://en.wikipedia.org/wiki/Time_dilation#Simple_inference: "Because all clocks that have a common period in the resting frame should have a common period when observed from the moving frame, all other clocks—mechanical, electronic, optical (such as an identical horizontal version of the clock in the example)—should exhibit the same velocity-dependent time dilation" — Mike_bb, Jun 22 '23 at 16:42

score 2 · Answer 3 · answered Jun 22 '23 at 13:00

Suppose you had some other type of clock that created "ticks" at some regular interval. You could calibrate this clock against a light clock; you might find that $N$ "ticks" of the light clock correspond to one "tick" of your new clock.

Suppose you then set this new clock and a light clock into uniform motion, and again did this same calibration procedure. This time you find that $N' \neq N$ "ticks" of the light clock correspond to one "tick" of your new clock. This would constitute an experiment you could do whose results differ between reference frames: in one reference frame the "conversion factor" is $N$ and in another reference frame it's $N'$.

But the axioms of relativity say that this isn't allowed; the laws of physics are supposed to be the same in all inertial reference frames, and the internal workings of your new clock (be it biological, mechanical, electrical, etc.) are governed by the laws of physics. The only way for this axiom to be satisfied is to have $N = N'$, which means that the time dilation effects will work exactly the same way on your new clock as they do on a light clock.

In fact, I highly doubt that anyone has actually ever done this experiment with an actual "light clock". All of the experimental evidence for time dilation that I'm aware of comes from observations of subatomic particles, or (in one case) atomic clocks.

How to prove that time slow down on all type of clocks?

3 Answers3